Problem: Find $w$, such that $5^65^w=25$.
Solution: The laws of exponents give us $5^65^w=5^{6+w}$.  And, because $25=5^2$, we have $5^{6+w}=5^2$.  It follows that $6+w=2$.  Subtracting 6 from both sides gives us $w=\boxed{-4}$.